In [1]:
import numpy as np
import numpy.random as rd
import matplotlib.pyplot as pl
import cvxpy as cvx
In [2]:
def gen_signal(n, s):
sigsparse = rd.randn(s)
pos = rd.choice(np.arange(n), size=s, replace=False)
sig = np.zeros(n)
sig[pos] = sigsparse
return sig
In [13]:
def recons(measurements, y, eta):
n = measurements.shape[1]
z = cvx.Variable(n)
objective = cvx.Minimize(cvx.norm2(measurements * z - y))
cons = [cvx.norm1(z) <= eta]
prob = cvx.Problem(objective, cons)
prob.solve()
return z.value
In [14]:
def random_experiment(n, s, m):
x = gen_signal(n, s)
measurements = np.random.randn(m, n)
f = lambda x: np.sign(x)
y = f(np.tensordot(measurements, x, axes=(1, 0)))
return x, recons(measurements, y, np.sqrt(s))
In [20]:
x, xsharp = random_experiment(500, 10, 800)
(800,)
In [16]:
x
Out[16]:
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In [19]:
np.max(np.abs(xsharp - np.sqrt(2 / np.pi) * x))
Out[19]:
1.5405987720799774
In [ ]:
Content source: dseuss/notebooks
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